Formula (According to Blender) to create an Enneper Order 3
From the formula here:

If a stands for n (so 3 in our case) and b for 2n-1 (so 5), then:
x = u*cos(v)-(u**b * cos(b*v) / b)

y = u*sin(v)+(u**b * sin(b*v) / b)

z = 2 * (u**a) * cos(a*v)/a

with:
0 &lt; u &lt; 1.2
-pi &lt; v &lt; pi

And:
a = 3
b = 2 * a - 1

Which is:

Then:

If you want to push u to its limits, set it between:
0 &lt; u &lt; sqrt(2)


And you can change the order setting a and b differently (b = 2 * a - 1), for instance:

If useful, here is the preset file &quot;enneper_n.py&quot; that can be stored into the preset directory (on Windows):
C:\Users\userName\AppData\Roaming\Blender Foundation\Blender\2.90\scripts\presets\operator\mesh.primitive_xyz_function_surface

Its content is:
import bpy
op = bpy.context.active_operator

op.x_eq = 'u*cos(v)-(u**b * cos(b*v) / b)'
op.y_eq = 'u*sin(v)+(u**b * sin(b*v) / b)'
op.z_eq = '2 * (u**a) * cos(a*v)/a'
op.range_u_min = 0.0
op.range_u_max = 1.2000000476837158
op.range_u_step = 32
op.wrap_u = False
op.range_v_min = -3.1415927410125732
op.range_v_max = 3.1415927410125732
op.range_v_step = 128
op.wrap_v = False
op.close_v = False
op.n_eq = 1
op.a_eq = '3'
op.b_eq = '2*a-1'
op.c_eq = '0'
op.f_eq = '0'
op.g_eq = '0'
op.h_eq = '0'
op.show_wire = True
op.edit_mode = False